[Embrio-list] Physics Informed Machine Learning at Today's Weekly

[Ladd, Brent Thomas]

Dear EMBRIO Folk:

Google Colab link for the mini-workshop part I at our Weekly today: Physics Informed Machine Learning led by Dr. Adrian Buganza Tepole. This builds to a degree from the previous two sessions (Part I<https://nam04.safelinks.protection.outlook.com/?url=https%3A%2F%2Fapp.box.com%2Fs%2Faojh22nsz7z901lbph6g6l6cb5voynnn&data=05%7C01%7Cembrio-list%40ecn.purdue.edu%7Cf1c113c24a1c4db12b4a08dbbdc3e293%7C4130bd397c53419cb1e58758d6d63f21%7C0%7C0%7C638312421233756952%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C3000%7C%7C%7C&sdata=7zvyQPZkxeEpMcpGqWLbGBj4I38G%2FxglpMbyoDyTXuE%3D&reserved=0>, Part II<https://nam04.safelinks.protection.outlook.com/?url=https%3A%2F%2Fapp.box.com%2Fs%2F7ppphpndazf4lz8qelo8oj9vuy2gz3t4&data=05%7C01%7Cembrio-list%40ecn.purdue.edu%7Cf1c113c24a1c4db12b4a08dbbdc3e293%7C4130bd397c53419cb1e58758d6d63f21%7C0%7C0%7C638312421233756952%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C3000%7C%7C%7C&sdata=AC6xNybHvO03SJ90d0V%2BaD1D75jxPffFU0cVAoxCh5E%3D&reserved=0>) on Solving ODEs and PDEs with Dr. Linlin Li.

https://colab.research.google.com/drive/1wloCgDIItT_BxDp4Gs5xvntNkshzCnAV?usp=sharing<https://nam04.safelinks.protection.outlook.com/?url=https%3A%2F%2Fcolab.research.google.com%2Fdrive%2F1wloCgDIItT_BxDp4Gs5xvntNkshzCnAV%3Fusp%3Dsharing&data=05%7C01%7Cembrio-list%40ecn.purdue.edu%7Cf1c113c24a1c4db12b4a08dbbdc3e293%7C4130bd397c53419cb1e58758d6d63f21%7C0%7C0%7C638312421233756952%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C3000%7C%7C%7C&sdata=z2lrTt9RSbiQ%2B2vYc0M9W2VruOKRkd2WpucgG3nBum0%3D&reserved=0>
[https://colab.research.google.com/img/colab_favicon_256px.png]<https://nam04.safelinks.protection.outlook.com/?url=https%3A%2F%2Fcolab.research.google.com%2Fdrive%2F1wloCgDIItT_BxDp4Gs5xvntNkshzCnAV%3Fusp%3Dsharing&data=05%7C01%7Cembrio-list%40ecn.purdue.edu%7Cf1c113c24a1c4db12b4a08dbbdc3e293%7C4130bd397c53419cb1e58758d6d63f21%7C0%7C0%7C638312421233913214%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C3000%7C%7C%7C&sdata=WnVpLo2LRysl75xxS%2F0zEL8g5FS23G6BKiA5xMXc4gg%3D&reserved=0>
Google Colaboratory<https://nam04.safelinks.protection.outlook.com/?url=https%3A%2F%2Fcolab.research.google.com%2Fdrive%2F1wloCgDIItT_BxDp4Gs5xvntNkshzCnAV%3Fusp%3Dsharing&data=05%7C01%7Cembrio-list%40ecn.purdue.edu%7Cf1c113c24a1c4db12b4a08dbbdc3e293%7C4130bd397c53419cb1e58758d6d63f21%7C0%7C0%7C638312421233913214%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C3000%7C%7C%7C&sdata=WnVpLo2LRysl75xxS%2F0zEL8g5FS23G6BKiA5xMXc4gg%3D&reserved=0>
colab.research.google.com
"Physics informed machine learning" led by Dr. Adrian Buganza Tepole starts today, September 25th during our Weekly meeting, with part II on October 2nd.

Mini workshop: Physics informed machine learning
Machine learning has impacted all fields of engineering. Artificial neural networks are universal function approximators. Thus, it is not surprising that they can be used to represent the types of functions that arise as solution of ordinary or partial differential equations (ODEs or PDEs respectively).

ODEs and PDEs are natural mathematical models for many physical phenomena such as diffusion, heat transfer, and mechanical equilibrium. Previous workshops as part of EMBRIO have already focused on the solution of ODEs and PDEs with more traditional methods, namely finite differences.

This workshop builds on that knowledge and explores the use of artificial neural networks for the solution of the same kinds of problems. We will introduce JAX, a numerical linear algebra package which is an alternative to other, perhaps more popular machine learning tools such as pytorch.

The reason to do the workshop around JAX is that this library allows for just-in-time compilation of code and vectorization which make it very efficient. Additionally, if attendees are familiar with the standard python packages numpy and scipy then JAX will hopefully require a less steep learning curve. Using JAX we will show that the PDEs of interest can be used as part of the loss function such that minimization of this objective yields the PDE solution.


Brent T. Ladd, Senior Research Program Manager, EMBRIO Institute<https://www.purdue.edu/research/embrio/>
Weldon School of Biomedical Engineering, Purdue University
Office: Hall for Discovery Learning and Research, Ste. 203
207 S. Martin Jischke Drive
West Lafayette, IN 47907
laddb at purdue.edu

<https://www.purdue.edu/research/embrio/>
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